Question

a triangle has interior angle measures of 86°, 4x, and 46°. what is the value of x?
write your answer as an integer or as a decimal rounded to the nearest tenth.
x =

Explanation:

Step1: Use the triangle angle - sum theorem

The sum of the interior angles of a triangle is \(180^{\circ}\). So, \(86 + 4x+46=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(86 + 46+4x=180\), which gives \(132 + 4x=180\).

Step3: Isolate the term with \(x\)

Subtract \(132\) from both sides: \(4x=180 - 132\). So, \(4x = 48\).

Step4: Solve for \(x\)

Divide both sides by \(4\): \(x=\frac{48}{4}\).

Answer:

\(x = 12\)